My laptop (Toshiba Satellite L750) just wont turn on, i've tried removing the battery and charger then holding down the power button, removing the battery and keeping the charger in, keeping the battery but no charger, but all to no avail.

Huh.... it is not easy to say what the problem is but probably power supply electronic is a “troublemaker”.
When you connect AC power supply is any of power LEDs ON?
Is something happened last days with your notebook? I mean we don’t know what have you done with your notebook.

I have had tthe same problem. Last time I borrowed the battery from a Toshiba L750 in work and it worked. Again this week the two white power lights are there and when I press the power button, they go out and the laptop is without any power!

Sounds not really good…
The unit should power up even the battery is removed but connected to AC adaptor.
Does the power led light while AC adaptor is connected?
If it does not light up then either your AC adaptor is faulty or motherboard problem.
If it light up but does not power up, then there is a problem with motherboard or part of motherboard (power supply electronic issue, etc…)

I see just one real option here: the tech guys from authorized service should take a look here…